University of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301Degree distance index of the Mycielskian and its complement19ENA.BehtoeiImam Khomeini International Universitya.behtoei@sci.ikiu.ac.irM.AnbarloeiImam Khomeini International Universitym.anbarloei@sci.ikiu.ac.ir10.22052/ijmc.2016.10845In this paper, we determine the degree distance of the complement of arbitrary Mycielskian graphs. It is well known that almost all graphs have diameter two. We determine this graphical invariant for the Mycielskian of graphs with diameter two.Degree distance,Zagreb indices,Mycielskianhttp://ijmc.kashanu.ac.ir/article_10845.htmlhttp://ijmc.kashanu.ac.ir/article_10845_4ba6f41aaf61461b68f1c3078233f5e5.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301A note on vertex-edge Wiener indices of graphs1117ENM.AzariKazerun Branch, Islamic Azad Universitymahdie.azari@gmail.com10.22052/ijmc.2016.11865The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact formulas for computing the vertex-edge Wiener indices of two composite graphs named splice and link.Distance in graph,Vertex-edge Wiener index,Splice,Linkhttp://ijmc.kashanu.ac.ir/article_11865.htmlhttp://ijmc.kashanu.ac.ir/article_11865_9080447f4b5e8d2998640cb39bf045d7.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301Electro-spunorganic nanofibers elaboration process investigations using BPs operational matrices1927ENH.JafariUniversity of Mazandaranjafari@umz.ac.irH.TajadodiUniversity of Sistan and Baluchestantajadodi@umz.ac.ir10.22052/ijmc.2016.11866In this paper operational matrix of Bernstein Polynomials (BPs) is used to solve Bratu equation. This nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. Elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. By using operational matrix of fractional integration and multiplication the investigated equations are turned into set of algebraic equations. Numerical solutions show both accuracy and simplicity of the suggested approach.Bratu equation,Elecotrospun nanofibers,Bernstein polynomials,operational matrixhttp://ijmc.kashanu.ac.ir/article_11866.htmlhttp://ijmc.kashanu.ac.ir/article_11866_914b2e89361dc43a0182ac89574aa076.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301Hosoya polynomials of random benzenoid chains2938ENS.-J.XuLanzhou Universityshjxu@lzu.edu.cnQ.-H.HeLanzhou Universityheqh12@lzu.edu.cnS.ZhouJiangsu Normal Universityzhous@lzu.edu.cnW.H.Chanwaihchan@ied.edu.hkwaihchan@ied.edu.hk10.22052/ijmc.2016.11867Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagons. Furthermore, as corollaries, the expected values of the well-known topological indices: Wiener index, hyper-Wiener index and Tratch-Stankevitch-Zefirov index of a random benzenoid chain with $n$ hexagons can be obtained by simple mathematical calculations, which generates the results given by I. Gutman et al. [Wiener numbers of random benzenoid chains, Chem. Phys. Lett. 173 (1990) 403-408].Wiener index,Random benzenoid chain,Hosoya polynomial,Expected value,Generating functionhttp://ijmc.kashanu.ac.ir/article_11867.htmlhttp://ijmc.kashanu.ac.ir/article_11867_e0847f53fd013808c54145717912481c.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301Complete forcing numbers of polyphenyl systems3946ENB.LiuSchool of Mathematical Sciences, Xinjiang Normal University,
Urumqi, Xinjiang 830054, P. R. China446297409@qq.comH.BianDepartment of Mathematics, Xinjiang Normal University,
Urumqi, Xinjiang 830054, P.R.Chinabh_1218@sina.comH.YuCollege of Mathematics and System Sciences, Xinjiang University,
Urumqi 830046, P.R.Chinayhz0611@163.com10.22052/ijmc.2016.11868The idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin squares, block designs and Steiner systems in combinatorics (see [1] and the references therein). Recently, the forcing on perfect matchings has been attracting more researchers attention. A forcing set of M is a subset of M contained in no other perfect matchings of G. A global forcing set of G, introduced by Vukiˇcevi´c et al., is a subset of E(G) on which there are distinct restrictions of any two different perfect matchings of G. Combining the above “forcing” and “global” ideas, Xu et al. [5] introduce and define a complete forcing set of G as a subset of E(G) on which the restriction of any perfect matching M of G is a forcing set of M. The minimum cardinality of complete forcing sets is the complete forcing number of G. In this paper, we give the explicit expressions for the complete forcing number of several classes of polyphenyl systems.Complete forcing number,Polyphenly system,Global forcing numberhttp://ijmc.kashanu.ac.ir/article_11868.htmlhttp://ijmc.kashanu.ac.ir/article_11868_5eb2b2f068c3fbac354c9f2fde2cfdd1.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301Quantitative structure activity relationship study of inhibitory activities of 5-lipoxygenase and design new compounds by different chemometrics methods4759ENF.Bagheban-ShahriChemistry,Arak Branch, Islamic Azad Universityf.baghebanshahri@gmail.comA.NiaziChemistry,Arak Branch, Islamic Azad Universitychemistrya10@gmail.comA.AkramiChemistry,Arak Branch, Islamic Azad Universityaahmad.akramii@gmail.com10.22052/ijmc.2016.11869A quantitative structure-activity relationship (QSAR) study was conducted for the prediction of inhibitory activity of 1-phenyl[2H]-tetrahydro-triazine-3-one analogues as inhibitors of 5-Lipoxygenase. The inhibitory activities of the 1-phenyl[2H]-tetrahydro-triazine-3-one analogues modeled as a function of molecular structures using chemometrics methods such as multiple linear regression (MLR) and least squares support vector machines (LS-SVM). The obtained models were applied to predict the inhibitory activity of compounds which were not in the modeling procedure. The results of models showed high prediction ability with root mean square error of prediction of 0.167 and 0.061 for MLR and LS-SVM, respectively. The LS-SVM method was used for prediction of inhibitory activity of the new inhibitor derivatives.QSAR,1-Phenyl[2H]-tetrahydro-triazine-3-oneanalogues,MLR,LS-SVMhttp://ijmc.kashanu.ac.ir/article_11869.htmlhttp://ijmc.kashanu.ac.ir/article_11869_1b5ded026dcd8a75a7cd052243b4ad72.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301Three-center Harary index and its applications6168ENB.FurtulaFaculty of Science, University of Kragujevacboris.furtula@gmail.comI.GutmanFaculty of Science, University of Kragujevac, Kragujevac, Serbiagutman@kg.ac.rsV.KatanicFaculty of Science, University of Kragujevacvlada.karanic@gmail.com10.22052/ijmc.2016.12402The Harary index H can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms, such that their magnitude decreases with the increasing distance between the respective two atoms. A generalization of the Harary index, denoted by Hk, is achieved by employing the Steiner-type distance between k-tuples of atoms. We show that the linear combination H+x H3 is significantly better correlated with a variety of physico-chemical properties of alkanes than H itself.Harary index,Multicenter Harary index,Steiner distance,Molecular Graphhttp://ijmc.kashanu.ac.ir/article_12402.htmlhttp://ijmc.kashanu.ac.ir/article_12402_ff64ec64188304a21bed1c7a4b1c22e4.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301Investigation the effect of nanocomposite material on permeation flux of polyerthersulfone membrane using a mathematical approach6975ENM.AdibPayame Noor University (PNU)marjan_ad_1360@yahoo.com10.22052/ijmc.2016.12403Integrally skinned asymmetric membranes based on nanocompositepolyethersulfone were prepared by the phase separation process using the supercritical CO2 as a nonsolvent for the polymer solution. In present study, the effects of temperature and nanoparticle on selectivity performance and permeability of gases has beeninvestigated. It is shown that the presence of silica nanoparticles not only disrupts the original polymer chain packing but also alters the chemical affinities of penetrants in polyethersulfone matrices. Because, in the presence of hydrophilic silica, CO2 affinity filler, hydrogen-bond interactions between the oxygen atoms of carbon dioxide and the hydrogen atoms of hydroxyl group on the nanosilica surface would take place at the interface and thus solubility and consequently permeability towards CO2 are higher in comparison with CH4 for the membranes. Furthermore, in present study, a novel mathematical approach has been proposed to develop a model for permeation flux and selectivity performance of the membrane using Support Vector Machine. SVM is employed to develop a model toestimateprocess output variables of a nanocomposite membrane including permeation flux and selectivity performance. Model development that consists of training, optimization and test was performed using randomly selected 80%, 10%, and 10% of available data respectively.Nanocomposite material • Polyerthersulfone membrane • Silica nanoparticles • Support Vector Machine (SVM)http://ijmc.kashanu.ac.ir/article_12403.htmlhttp://ijmc.kashanu.ac.ir/article_12403_a9874c07a28f1c3c7b67ab286aecd0d9.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301On the generalized mass transfer with a chemical reaction: Fractional derivative model7788ENA.AnsariShahrekord University, P.O.Box 115, Shahrekord, Iranalireza_1038@yahoo.comM.Ahmadi DaraniDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
Shahrekord University, P.O.Box 115, Shahrekord, Iranfarshidahmadi633@gmail.com10.22052/ijmc.2016.12404In this article using the inverse Laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. These transfers have been expressed as the Couette flow with the fractional derivative of the Caputo sense. Also, using the Hankel contour for the Bromwich's integral, the solutions are given in terms of the generalized Airy functions.Lévêque Problem,Laplace transform,Generalized Airy functions,Fractional derivativehttp://ijmc.kashanu.ac.ir/article_12404.htmlhttp://ijmc.kashanu.ac.ir/article_12404_412497ee8587a49f897a821ff5f751f8.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301A note on hyper-Zagreb index of graph operations8992ENB.BasavanagoudKARNATAK UNIVERSITY DHARWADb.basavanagoud@gmail.comS.PatilKARNATAK UNIVERSITY, DHARWADshreekantpatil949@gmail.com10.22052/ijmc.2016.12405In this paper, the Hyper - Zagreb index of the Cartesian product, composition and corona product of graphs are computed. These corrects some errors in G. H. Shirdel et al.[11].Hyper-Zagreb index,Zagreb index,Graph operationhttp://ijmc.kashanu.ac.ir/article_12405.htmlhttp://ijmc.kashanu.ac.ir/article_12405_2b6320568ffc299789173e21593336db.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90157120160301QSPR study on benzene derivatives to some physico-chemical properties by using topological indices93110ENM.Pashm ForushIslamic Azad UnivF.ShafieiIslamic Azad Univshafa38@yahoo.comF.DialamehpourIslamic Azad Univfd200988@yahoo.com10.22052/ijmc.2016.12410QSPR study on benzene derivatives have been made using recently introduced topological methodology. In this study the relationship between the Randic' (x'), Balaban (J), Szeged (Sz),Harary (H), Wiener (W), HyperWiener and Wiener Polarity (WP) to the thermal energy (Eth), heat capacity (CV) and entropy (S) of benzene derivatives is represented. Physicochemical properties are taken from the quantum mechanics methodology with HF level using the ab initio 6-31G basis sets. The multiple linear regressions (MLR) and back ward methods (with significant at the 0.05 level) were employed to give the QSPR models. The satisfactory obtained results show that combining the two descriptors (Sz, HW) are useful topological descriptors for predicted (CV) and (S) of the 45 benzene derivatives. The training set models established by MLR method have not good correlation of (Eth), which means QSPR models could not predict the thermal energy of compounds.QSPR,Topological indices,Benzene derivatives,Graph theory,Multiple linear regressions (MLR)http://ijmc.kashanu.ac.ir/article_12410.htmlhttp://ijmc.kashanu.ac.ir/article_12410_d4fb17c9ff5de612df4bd46f3053f2c6.pdf